Sounding reference signal processing for lte

ABSTRACT

A wireless communication receiver including a serial to parallel converter receiving an radio frequency signal, a fast Fourier transform device connected to said serial to parallel converter converting N FFT  corresponding serial signals into a frequency domain; an EZC root sequence unit generating a set of root sequence signals; an element-by-element multiply unit forming a set of products including a product of each of said frequency domain signals from said fast Fourier transform device and a corresponding root sequence signal, an N SRS -length IDFT unit performing a group cyclic-shift de-multiplexing of the products and a discrete Fourier transform unit converting connected cyclic shift de-multiplexing signals back to frequency-domain.

CLAIM OF PRIORITY

This application claims priority under 35 U.S.C. 119(e)(1) to U.S.Provisional Application No. 61/406,233 filed Oct. 25, 2010 and U.S.Provisional Application No. 61/437,744 filed Jan. 31, 2011.

TECHNICAL FIELD OF THE INVENTION

The technical field of this invention is wireless communication.

BACKGROUND OF THE INVENTION

Evolved Universal Terrestrial Radio Access Network (E-UTRAN) Long TermEvolution (LTE) wireless networks were standardized by the 3GPP workinggroups (WG). Orthogonal Frequency Division Multiple Access (OFDMA) andsingle carrier Frequency Division Multiple Access (SC-FDMA) accessschemes were chosen for the down-link (DL) and up-link (UL) of E-UTRAN,respectively. User Equipments (UE's) are time and frequency multiplexedon a physical uplink shared channel (PUSCH) and a physical uplinkcontrol channel (PUCCH), and time and frequency synchronization betweenUE's guarantees optimal intra-cell orthogonality. An important ULreference signal, the Sounding Reference Signal (SRS) is defined insupport of frequency dependent scheduling, link adaptation, powercontrol and UL synchronization maintenance, which are functions handledabove the Physical Layer, mainly at layer 2. Indeed, the main purpose ofthis signal is to allow the Base Station, also referred to as eNodeB,estimating a UE's radio channel information on time and frequencyresources possibly different from those where it is scheduled. SRSprocessing occurs at the Physical Layer though and delivers to upperlayers mainly three metrics estimated from the SRS:

-   -   Channel estimates and gains across the system bandwidth;    -   Noise variance; and    -   Timing offset.        SRS processing may compute and deliver from the first two items        a signal to interference plus noise ratio (SINR) measurement.

Both UL MU-MIMO/SIMO and DL eigen-beamforming based schedulers rely onthe SRS to get the UE's channel estimates and derive the relevantscheduling metric. In particular, for the broadly deployed baseline SIMOUL scheduler, the scheduler makes use of the UE's signal to interferenceplus noise ratio (SINR) information to compute the scheduling metric andperform link adaptation. The UE's SINR can be directly derived from thefirst two above metrics or can use additional interference estimatesfrom other reference signals such as the Demodulation Reference Signal(DMRS). The MAC sub-layer uses and potentially accumulates over time thetiming offset estimates to issue a Timing Advance (TA) command to theUE, as a MAC control element. Sounding reference signal is also referredto as sounding reference symbol. Within this patent application the termchannel quality indicator (CQI) is interchangeable with channel stateindicator (CSI), channel state and channel value.

SUMMARY OF THE INVENTION

This invention is an algorithm to estimate the above metrics, assesstheir performance and analyze the different ways to estimate UE's SNRbased on these metrics. This invention describes details in the designchoices for the LTE SRS channel, channel gain, noise variance and timingoffset estimators, from theoretical derivations and performanceevaluations. In particular, this invention shows that the proposedtime-domain based channel estimation with group-UE cyclic shiftde-multiplexing is a low-complexity approach that allows sharing thesame upfront computation for users' channels and timing offsetestimations, as well as noise variance estimation. Unbiased channel gainestimation requires estimating and removing the noise variance by meansof one reserved cyclic shift per SRS comb. Performance results obtainedfrom realistic multi-user link-level simulations over a wide SNR rangeare presented and can be used for further reference in systemsimulations, such as UL scheduling, to model the channel estimationerror from SRS. This invention includes:

1. A time-domain based SRS receiver at the eNB with group-UE cyclicshift de-multiplexing formulated as per Equations (2) and (3) producingfor each SRS comb the concatenated CIRs sequence y of all UEsmultiplexed on the same root sequence and which structure is defined inFIG. 4;

2. A per-antenna per-sub-carrier frequency-domain channel estimationalgorithm formulated as per Equations (4) and (5) involving zeroing-outy samples outside the cyclic shift window of user u and last stageN_(SRS)-length DFT-based frequency interpolation;

3. User cyclic shift window design coping with spill-over effects user uas well as adjacent users and timing uncertainties, as shown in FIG. 5and FIG. 37;

4. Collecting the channel estimates over the SRS bandwidth shrunk by anamount typically set to 10% to minimize the interpolation errors;

5. A non-biased per-antenna per-sub-carrier channel gain estimatorformulated as per Equation (14) involving estimating and removing thenoise variance;

6. A noise removal technique with negative gain avoidance by applying asimple clipping threshold of 0.01, as shown in Equation (16);

7. A per-antenna time domain noise variance estimator formulated as perEquation (18) involving reserving a cyclic shift per SRS comb, andaveraging the squared noise samples across a noise window selected fromy;

8. A noise window design maximizing the number of noise samples whilenot including samples carrying adjacent users' energy such as e.g. inspill-over regions, as shown in FIG. 10;

9. A noise reduction technique consisting in UE-geometry-based selectivecyclic shift window reduction as shown in Table 3;

10. A per-chunk SNR estimator from the achieved per-antennaper-subcarrier channel gain estimates based on selectively usinglow-complexity arithmetic averaging (33) or harmonic averaging (32)depending on both the channel type and the UE's SNR;

11. A timing offset estimator combining the amplitude delay profilesacross antennas from the concatenated delay profiles sequence y andsearching for the highest peak in the user's timing offset window, asshown in Equation (35);

12. A timing offset window design taking the main energy region withinthe delay spread window, enlarged on both sides by the maximum expectedtiming offset, as shown in Equation (36);

13. The above are not restricted to LTE, but can be applied to anywireless network.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of this invention are illustrated in thedrawings, in which:

FIG. 1 illustrates an exemplary prior art wireless communication systemto which this application is applicable;

FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA)Time Division Duplex (TDD) frame structure of the prior art;

FIGS. 3A and 3B illustrate SRS frequency configurations in 20 MHz systembandwidth for C_(SRS)=1 and C_(SRS)=2;

FIG. 4 is an LTE sub-frame structure;

FIG. 5 illustrates the transmitter of this invention;

FIG. 6 illustrates a SRS receiver of this invention;

FIGS. 7A and 7B illustrate the case of four cyclic-shift multiplexed UEsper SRS comb with 5 μS delay spread TU channel;

FIGS. 8A and 8B illustrate two plots of the real and imaginarycomponents for actual data and estimated data versus sub-carrier, FIG.8A the TU channel and FIG. 8B the PA channel;

FIGS. 9A and 9B illustrate two plots of mean squared error of ChannelQuality Index (CQI) value in dB versus sub-carrier, FIG. 9A the TUchannel and FIG. 9B the PA channel;

FIGS. 10A and 10B illustrate plots of Channel estimation Mean SquaredError in Channel Quality Indicator (CQI) estimates of the shrunkbandwidth in dB versus signal to noise ratio (SNR) in dB, FIG. 10A theTU channel and FIG. 10B the PA channel;

FIGS. 11A and 11B illustrate a plot of mean square error of CQI estimateversus signal to noise ratio, FIG. 11A the TU channel and FIG. 11B thePA channel;

FIG. 12 shows a plot of power delay profile versus time samples;

FIGS. 13A and 13B illustrate plots of channel gain estimate mean errorversus signal to noise ratio in dB for the TU channel (FIG. 13A) and forthe PA channel (FIG. 13B);

FIGS. 14A and 14B show the channel gain estimation error with andwithout noise variance estimation removal for both the TU channel (FIG.14A) and the PA channel (FIG. 14B) for varying the number of SRS usersat 20 PRB SRS bandwidth;

FIGS. 15A and 15B illustrate the mean channel gain estimation error(FIG. 15A) and standard deviation of the channel gain estimation error(FIG. 15B) versus signal to noise ratio in dB for various gainestimation techniques for the TU channel;

FIGS. 16A and 16B illustrate the mean channel gain estimation error(FIG. 16A) and standard deviation of the channel gain estimation error(FIG. 16B) versus signal to noise ratio in dB for various gainestimation techniques for the PA channel;

FIG. 17 plots the normalized MSE performance mean square error σ_(H) ²of the channel estimates Ĥ per sub-carrier per antenna in dB versussignal to noise ratio in dB for two SRS users;

FIGS. 18A and 18B are two plots of channel gain estimation mean error(FIG. 18A) and channel gain estimation standard deviation of error (FIG.18B) versus signal to noise ratio in dB for systems with two SRS users;

FIGS. 19A and 19B plot the normalized MSE performance σ_(H) ² of thechannel estimates Ĥ versus signal to noise ratio per sub-carrier perantenna for various window shrink amounts, FIG. 19A is the TU channel,FIG. 19B is the PA channel;

FIGS. 20A and 20B illustrate plots of the mean errors of the channelgain estimator versus signal to noise ratio in dB, FIG. 20A is the TUchannel, FIG. 20B is the PA channel.

FIGS. 21A and 21B illustrate plots of the standard deviation of thechannel gain estimator versus signal to noise ratio in dB, FIG. 21A isthe TU channel, FIG. 21B is the PA channel;

FIGS. 22A and 22B illustrate plots of the mean square error in channelestimate error versus signal to noise ratio for various conditions

FIGS. 23A and 23B illustrate plots of the standard deviation in channelestimate error versus signal to noise ratio for various conditions;

FIGS. 24A and 24B illustrate plots of the standard deviation of thechannel gain estimator versus signal to noise ratio in dB;

FIG. 25 illustrates mean square error of channel estimates for 4-PRB SRSbandwidth and 80% cyclic shift window shrink versus signal to noiseratio;

FIGS. 26A and 26B illustrate channel gain estimation mean error (FIG.26A) and standard deviation channel gain estimation error (FIG. 26B)versus signal to noise ratio;

FIG. 27 illustrates plots of mean square error in channel estimationversus signal to noise ratio with and without least mean squaredfiltering;

FIGS. 28A and 28B illustrate the mean channel gain estimation error(FIG. 28A) and standard deviation of the channel gain estimation error(FIG. 28B) versus signal to noise ratio in dB for various LMStechniques;

FIGS. 29A and 29B illustrate the mean square error of channel estimationversus signal to noise ratio for various number of SRS users for 20-PRBSRS bandwidth (FIG. 29A) and for 6 TU channel users and 14 PA channelusers (FIG. 29B);

FIGS. 30A and 30B illustrate the channel gain estimation mean errorversus signal to noise ratio for various number of SRS users for 20-PRBSRS bandwidth (FIG. 30A) and for 6 TU channel users and 14 PA channelusers (FIG. 30B);

FIGS. 31A and 31B illustrate the channel gain estimation standarddeviation versus signal to noise ratio for various number of SRS usersfor 20-PRB SRS bandwidth (FIG. 31A) and for 6 TU channel users and 14 PAchannel users (FIG. 31B);

FIGS. 32A and 32B show mean signal to noise error (FIG. 32A) andstandard deviation of the signal to noise error (FIG. 32B) versus signalto noise ratio for various conditions with 20 PRB SRS bandwidth and 2SRS users per symbol;

FIGS. 33A and 33B are the mean chuck SNR error versus signal to noiseratio for various chunk averaging, FIG. 33A is the TU channel, FIG. 33Bis the PA channel;

FIGS. 34A and 34B are the standard deviation of the chuck SNR errorversus signal to noise ratio for various chunk averaging, FIG. 34A inthe TU channel, FIG. 34B is the PA channel;

FIG. 35 illustrates decimated samples centered in the PRB;

FIGS. 36A and 36B show the performance of the per-PRB SNR estimator{circumflex over (ρ)}_(ch-H) (chunk size=1 PRB) when sub-carrierdecimation is applied during the harmonic averaging, for 20-PRB SRSbandwidth and when running 6 and 14 SRS users per symbol for both the TUchannel and the PA channel for mean chunk SNR error versus signal tonoise ratio (FIG. 36A) and for the standard deviation of the chunk SNRerror versus signal to noise ratio (FIG. 36B);

FIGS. 37A and 37B illustrate the mean chunk SNR error versus signal tonoise ratio for various number of SRS users for 20-PRB SRS bandwidth(FIG. 37A) and for 6 TU channel users and 14 PA channel users (FIG.37B):

FIGS. 38A and 38B illustrate the standard deviation of the chunk SNRerror versus signal to noise ratio for various number of SRS users for20-PRB SRS bandwidth (FIG. 38A) and for 6 TU channel users and 14 PAchannel users (FIG. 38B);

FIG. 39 illustrates that in presence of timing errors, the user cyclicshift window n₁(u), . . . , n_(L)(u) for the case of four cyclic-shiftmultiplexed UEs per SRS comb with 5 μS delay spread TU channel;

FIGS. 40A and 40B illustrate the performance degradation of the per-PRBSNR estimation with no sub-carrier decimation, in presence of timingerrors, for 20-PRB SRS bandwidth and when running 6 and 14 SRS users persymbol for both the TU channel and the PA channel, FIG. 40A is the meanchunk SNR error, FIG. 40B is the standard deviation of the chunk SNRerror;

FIGS. 41A and 41B illustrate the impact of narrowing the SRS bandwidthdown to 4 PRBs which further reduces the user cyclic shift window size,in presence of timing errors of ±0.5 μS, FIG. 41A is the mean chunk SNRerror and FIG. 41B is the standard deviation of the mean chunk SNRerror;

FIG. 42 show a plot of power delay profile versus time samples;

FIGS. 43A and 43B are the average demultiplexed power delay profile forthe TU channel (FIG. 43A) and the PA channel (FIG. 43B) versus delay forvarious SRS bandwidths;

FIGS. 44A and 44B plot the timing estimation mean and standard deviationerrors of the described algorithm for both the TU channel and the PAchannel when varying the SRS bandwidth, FIG. 44A shows the timing offsetmean and FIG. 44B shows the timing offset standard deviation;

FIGS. 45A through 45D respectively plot the CDF of the timing estimationerror from the described algorithm for both TU and PA channels at −18,−12, −6 and 0 dB E_(s)/N₀, when varying the SRS bandwidth;

FIG. 46 is a block diagram illustrating internal details of a basestation and a mobile user equipment in the network system of FIG. 1suitable for implementing this invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 shows an exemplary wireless telecommunications network 100. Theillustrative telecommunications network includes base stations 101, 102and 103, though in operation, a telecommunications network necessarilyincludes many more base stations. Each of base stations 101, 102 and 103(eNB) are operable over corresponding coverage areas 104, 105 and 106.Each base station's coverage area is further divided into cells. In theillustrated network, each base station's coverage area is divided intothree cells. Handset or other user equipment (UE) 109 is shown in Cell A108. Cell A 108 is within coverage area 104 of base station 101. Basestation 101 transmits to and receives transmissions from UE 109. As UE109 moves out of Cell A 108 and into Cell B 107, UE 109 may be handedover to base station 102. Because UE 109 is synchronized with basestation 101, UE 109 can employ non-synchronized random access toinitiate handover to base station 102.

Non-synchronized UE 109 also employs non-synchronous random access torequest allocation of up-link 111 time or frequency or code resources.If UE 109 has data ready for transmission, which may be traffic data,measurements report, tracking area update, UE 109 can transmit a randomaccess signal on up-link 111. The random access signal notifies basestation 101 that UE 109 requires up-link resources to transmit the UEsdata. Base station 101 responds by transmitting to UE 109 via down-link110, a message containing the parameters of the resources allocated forUE 109 up-link transmission along with a possible timing errorcorrection. After receiving the resource allocation and a possibletiming advance message transmitted on down-link 110 by base station 101,UE 109 optionally adjusts its transmit timing and transmits the data onup-link 111 employing the allotted resources during the prescribed timeinterval.

Base station 101 configures UE 109 for periodic uplink soundingreference signal (SRS) transmission. Base station 101 estimates uplinkchannel state information (CSI) from the SRS transmission.

FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA)time division duplex (TDD) Frame Structure. Different subframes areallocated for downlink (DL) or uplink (UL) transmissions. Table 1 showsapplicable DL/UL subframe allocations.

TABLE 1 Switch- Config- point Sub-frame number uration periodicity 0 1 23 4 5 6 7 8 9 0  5 ms D S U U U D S U U U 1  5 ms D S U U D D S U U D 2 5 ms D S U D D D S U D D 3 10 ms D S U U U D D D D D 4 10 ms D S U U DD D D D D 5 10 ms D S U D D D D D D D 6 10 ms D S U U U D S U U D

Sounding Reference Signal Bandwidths Configurations

In LTE, a UE can be Radio Resource Control (RRC) assigned either of thefour possible sounding bandwidths for a given cell-specific SRSbandwidth configuration C_(SRS) and system bandwidth. For each group ofsystem bandwidths, there are eight SRS bandwidth configurations C_(SRS)corresponding to different system bandwidths and/or ratios ofPUCCH/PUSCH region sizes. The larger C_(SRS) the smaller the total SRSbandwidth. For each SRS bandwidth configuration the four possiblesounding bandwidths are denoted m_(SRS,0), m_(SRS,1), m_(SRS,2),m_(SRS,3) ordered by decreasing size and are expressed in physicalresource blocks (PRB) of size N_(sc) ^(RB)=12 sub-carriers. The quantitym_(SRS,0) defines the largest possible SRS bandwidth. The quantitym_(SRS,0) along with the sub-carrier offset k′₀ defines the bandwidthregion. No combination of smaller bandwidths exceeds this region. Thequantities m_(SRS,0), m_(SRS,1), and m_(SRS,2) are defined to allow somekind of dichotomy providing a way to split the total sounding bandwidthinto 2, 3, 4 or 6 scheduling bandwidths (FIG. 3). This allows splittingthe total number of UEs in the scheduler pool into equally spacedbandwidths and running as many parallel schedulers concurrently. Thequantity m_(SRS,3) is always 4 PRBs and is mainly for power limited UEs.

FIGS. 3A and 3B together illustrate two plots of RRC frequency domainposition index (n_RRC) versus starting subcarrier. FIGS. 3A and 3Billustrate SRS frequency configurations in 20 MHz system bandwidth withC_(SRS)=1 (FIG. 3A) and C_(SRS)=2 (FIG. 3B). Each plot has curves for 1SRS band, 2 SRS bands, 3 SRS bands and 4 SRS bands.

For scenarios reflecting peak data rates situations, it is safe toassume no power limitation at the UE from the sounding perspective andstick to the combinations of m m_(SRS,1) and m_(SRS,2). For a 20 MHzspectrum and PUCCH occupying 8 PRBs, an appropriate combination ofm_(SRS,0), m_(SRS,1) and m_(SRS,2) is 80/40/20 PRBs (C_(SRS)=2). Thisallows multiplexing the largest number of SRSs per sub-frame bysplitting the total bandwidth into four 20-PRB scheduling bandwidthseach of large-enough size (3.6 MHz) to provide sufficient frequencyselective gains. For tougher propagation conditions, such as LTE Case 1,configurations allowing smaller SRS bandwidths for m_(SRS,0), m_(SRS,1)and m_(SRS,2) might be preferred to provide more flexibility inallocating UEs with different levels of power limitations. For example,C_(SRS)=7 specifies 48/16/8/4 PRBs for respective SRS bandwidthsm_(SRS,0), m_(SRS,1), m_(SRS,2) and m_(SRS,0).

SRS Design for LTE

An LTE sub-frame structure is depicted in FIG. 4. Each sub-frame 410includes two 0.5 ms slots. 401 and 402. Each slot 401 and 402 is made ofsix Discrete Fourier Transform (DFT) Spread Orthogonal FrequencyDivision Multiplexing (SOFDM) data symbols and one central demodulationreference symbol (DMRS). When the sub-frame 410 is configured for SRStransmission, the last symbol number 14 is reserved for SRStransmission.

Multiple UEs can be multiplexed in the same SRS symbol. The multiplexingscheme is a combination of FDM and Code Division Multiplexing (CDM).FIG. 5 illustrates this transmission technique. The sounding signal isbuilt from a pilot root sequence of length NSRS from EZC root sequenceunit 501. EZC root sequence unit 501 generates an extended Zadoff-Chu(EZC) sequence constructed by extending the closest prime-lengthZadoff-Chu (ZC) sequence to the SRS sequence length N_(SRS) providingthe configured SRS bandwidth. Such sequence has Constant Amplitude ZeroAutocorrelation (CAZAC) properties. This property guarantees discreteperiodic autocorrelations are zero for all non-zero lags, allowingorthogonal code multiplexing by duplicating and cyclic shifting the sameroot sequence. The constant amplitude property allows controlling thePeak-to-Average Power Ratio (PAPR) and generates bounded and time-flatinterference to other users. In a given sub-frame, all UEs in the samecell and with the same SRS bandwidth share the same root EZC sequenceX=(X₀, X₀, . . . , X_(N) _(SRS) ⁻¹)^(T), defined in frequency domain.Then, the sequence is modified per Equation (1) in time-domain cyclicshift unit 502 so as to produce a cyclic shift C_(u)=N_(SRS)m(u)/8 intime-domain, configured for user u, and where 8 is the CDM multiplexingcapacity:

X _(u,k) =X _(k) e ^(j2πkm(u)/8) ; m(u)ε{0 . . . 7}  (1)

The resulting sequence is further mapped to the N_(SRS) sub-carriersallocated to SRS out of N_(FFT) in inverse Fast Fourier Transform (IFFT)unit 503. Here N_(FFT) is the total amount of sub-carriers of the systembandwidth. N_(FFT)=2048 for a 20 MHz LTE system bandwidth. The tonemapping also reflects the Single Carrier Interleaved Frequency DivisionMultiple Access (SC-IFDMA) transmission scheme of the SRS. Within itsallocated bandwidth, a UE's SRS sequence is mapped on every other tone,leaving in-between tones to zero. This produces the two combs per SRSbandwidth illustrated in FIG. 7. This is one aspect of the FDMmultiplex, the other aspect being that different UEs can send their SRSon different bandwidths. As a result, the total SRS multiplexingcapacity for a given SRS bandwidth is 8 (CDM) times 2 (FDM)=16. With theIFDM multiplexing scheme, the sequence duration equals half the OFDMsymbol duration T. Hence, in LTE where T=66.67 μs, the minimum cyclicshift increment between two CDM'ed users is T/2/8=4.17 μs. Parallel toserial converter 504 generates that radio frequency (RF) coupled to theantenna (not shown).

SRS Receive Structure

FIG. 6 illustrates a SRS receiver. Serial to parallel converter 601converts the received RF into serial data streams. Each received timesample sequence r is converted in frequency domain through anN_(FFT)-length FFT (FFT 602). EZC root sequence unit 603 generates aroot sequence corresponding to the root sequence of EZC root sequenceunit 501. Element-wise multiply unit 604 multiplies correspondingelements of the RF input with the root sequence. This de-mapsSRS-relevant sub-carriers to produce a frequency-domain sequence Ycarrying all CDM users. Y is then converted back to time domain sequencey through N_(SRS)-length IDFT 605. This performs cyclic-shiftde-multiplexing for each of the 8 CDM'ed users. In particular, thisproposed system takes profit of the SRS OFDM symbol structure and CAZACsequence to compute each multiplexed UE's channel impulse response (CIR)through a frequency-domain computed periodic correlation (matchedfilter). Frequency-domain channel estimates are then obtained byextracting each user's relevant samples from the total CIR samples andconverting them back to frequency-domain through N_(SRS)-length DFT 606.This method is referred to as time-domain based channel estimation.

The SRS receiver of this invention (FIG. 6) follows the same principleas the prior art with an additional complexity reduction achieved fromgroup-UE cyclic shift de-multiplexing. Rather than correlating y witheach UE's sequence, the received frequency-domain sequence Y iselement-wise multiplied with the complex conjugate of the expected rootsequence X (element-wise multiply unit 604) before the IDFT, asillustrated in FIG. 6. This provides in one shot the concatenated CIRsof all UEs multiplexed on the same root sequence. Cyclic-shiftde-multiplexing reduces to selecting the relevant samples for each UE.This method can be expressed as:

Y=F _(N) _(SRS) _(N) _(FFT) r  (2)

y=F _(N) _(SRS) ⁻¹diag(X*Y ^(T))  (3)

y _(u)=(0, . . . ;0,y _(n) ₁ _((u)) ,y _(n) ₂ _((u)) , . . . ;y _(n)_(L) _((u)),0, . . . ;0)^(T)  (4)

Ĥ _(u) =F _(N) _(SRS) y _(u)  (5)

where: N_(SRS) by N_(FFT) matrix F_(N) _(SRS) _(N) _(FFT) corresponds toN_(FFT)-point FFT and N_(SRS) sub-carriers de-mapping; N_(SRS) byN_(SRS) matrixes F_(N) _(SRS) and F_(N) _(SRS) ⁻¹ correspond toN_(SRS)-point DFT and IDFT respectively; n₁(u), . . . , n_(L)(u) are thesamples defining the cyclic shift window of user u; and L is the numberof time samples corresponding to the maximum expected delay spread amongusers derived from the delay spread τ, the pad δ taken to account forthe delay spread spill-over in the window, the symbol duration T and thenumber of SRS sub-carriers per comb N_(SRS) as:

L=┌2(τ+δ)N _(SRS) /T┐  (6)

Table 2 shows the resulting values of L for different channels and SRSbandwidths examples assuming a spill-over pad δ=0.55 μS (measuredempirically). Table 2 shows the number of cyclic shift window samplesfor various configurations.

TABLE 2 SRS BANDWIDTH (PRBS) Delay 20 8 4 spread τ 5 0.9 5 0.9 5 0.9(μS) (TU) (PA) (TU) (PA) (TU) (PA) L (samples) 20 6 8 3 4 2FIG. 7 illustrates the case of four cyclic-shift multiplexed UEs per SRScomb with 5 μS delay spread TU channel. The top part of FIG. 7 shows aplot of power delay profile versus time sample for four user windows.The bottom part of FIG. 7 shows a plot of demultiplexed power delayprofile versus the same time samples. In FIG. 7 the user CIR extractionand cyclic shift de-multiplexing are performed simultaneously byselecting the appropriate user's cyclic shift window from theconcatenated time-domain CIRs sequence y of all multiplexed UEs. Thismethod is compared with the conventional frequency-domain channelestimation approach, where the cyclic shift de-multiplexing is performeddirectly onto the de-mapped frequency-domain sequence Y acrosssub-carrier chunks to produce channel estimate chunks as follows:

Ĥ _(u)(c)=X _(u) ^(H)(c)F _(N) _(c) _(N) _(FFT) r  (7)

where: Ĥ_(u)(c) is the channel estimate across chunk c spanningsub-carriers n₁(c), . . . , n_(c)(c); C is the chunk size X_(u)(c)=(0, .. . , 0, X_(n) ₁ _((c)), X_(n) ₂ _((c)), . . . , X_(n) _(C) _((c)), 0, .. . , 0)^(T); and the N_(c) by N_(FFT) matrix F_(N) _(c) _(N) _(FFT)corresponds to N_(FFT)-point FFT and N_(c) sub-carriers de-mapping.

Compared to the frequency-domain channel estimation approach,zeroing-out samples outside the user's energy window in this inventionachieve multiple benefits.

Channel Estimates Per Sub-Carrier

The last stage N_(SRS)-length DFT-based frequency interpolation provideschannel estimates on each of the N_(SRS) sub-carriers. Per-chunk channelestimates obtained with the frequency-domain approach are averagedarithmetically across the chunk sub-carriers. This disallows harmonicaveraging of the user's SINR as requested by the UL scheduler toestimate the user's throughput with MMSE receiver.

Channel Estimation MSE Reduction

With the last stage N_(SRS)-length DFT, the energy of the Additive WhiteGaussian Noise (AWGN) samples in the user's window is spread across theN_(SRS) sub-carriers. Since the user's energy is all contained in itscyclic shift window, this represents a reduction factor G_(σ) _(H) ₂ onthe channel estimation mean square error (MSE) σ_(H) ² of N_(SRS)/Lcorresponding to the ratio of half the OFDM symbol duration T/2 (due toIFDM with 2 combs per symbol) over the maximum expected delay spread τamong users:

$\begin{matrix}{G_{\sigma_{H}^{2}} = \frac{T}{2\tau}} & (8)\end{matrix}$

With a LTE symbol duration of 66.67 μS and TU channel delay spread of 5μS, an MSE improvement close to 8 dB is achieved for the channelestimation.

Channel Estimation Performance

The following is an evaluation of the performance of the invention in arealistic multi-user SC-FDMA multiplex simulation. The simulator modelsa number of UEs multiplexed on a configurable SRS bandwidth within thetotal bandwidth (25 PRBs) available in 5 MHz spectrum. The rootsequence, cyclic shift and frequency mapping of the UEs are re-selectedrandomly every sub-frame. The simulator models timing errors of the UEschosen randomly within a maximum time uncertainty window. The SNR ismeasured in time domain and is representative of the average signalpower across the SRS bandwidth, not in the user's comb only. Table 3below includes all parameters of the simulation.

TABLE 3 Parameter Value or range System Bandwidth 5 MHz Number ofantennas 2 Number of SRS users 2-16 SRS bandwidths 4 - 8 - 20 PRBsScheduled sub-frames per UE All SRS sequences EZC with random selectionof ZC index and cyclic shift every sub-frame Max timing uncertainty +/−1μs window Channels AWGN, TU6, PA UE speed 3 km/hThis evaluation uses for performance criterions the normalized meansquare error of the channel estimates Ĥ per sub-carrier per antenna:

$\begin{matrix}{\sigma_{H}^{2} = \frac{E\left\{ {{\hat{H} - H}}^{2} \right\}}{a^{2}}} & (9)\end{matrix}$

where: a²=E{|H|²} is the averaged received power from the user.

Channel Estimator Distortions

A first simulation assesses the performance of the proposed estimator inabsence of noise. The time-domain approach of this invention requiresthat the channel be first down-sampled to time domain and theninterpolated to frequency domain. The former acts as a sinc band-passfilter on the channel, which has two consequences:

-   -   The narrower the SRS bandwidth, the coarser the CIR and        therefore the channel estimates; and    -   Some spill-over effects should be accounted for when designing        the user window for cyclic shift de-multiplexing. This        spill-over leads to non-perfect orthogonality between cyclic        shifts.        The latter unavoidably creates interpolation errors at both ends        of the interpolation such as SRS bandwidth edges. FIGS. 8A, 8B,        9A and 9B illustrate this. FIG. 8 illustrates two plots of the        real and imaginary components for actual data and estimated data        versus sub-carrier. FIG. 8A is the TU channel. FIG. 8B is the PA        channel. FIG. 8 illustrates four curves; the X component        channel; the X component estimate; the Y component channel and        the Y component estimate. FIGS. 8A and 8B illustrate regions        811, 812, 821 and 822 of larger errors.

Due to the larger error regions illustrated in FIGS. 8A and 8B it isrecommended to reduce the scope of the channel estimation to the innerSRS bandwidth only. FIG. 9 illustrates two plots of mean squared errorof the channel estimates Ĥ per sub-carrier per antenna, known as ChannelQuality Index (CQI) value, in dB versus sub-carrier. FIG. 9A is the TUchannel. FIG. 9B is the PA channel. FIG. 9 illustrates four curves; twoSRS users; four SRS users; 8 SRS users; and 16 SRS users. FIGS. 9A and9B illustrate regions 911 and 921 of larger errors. As seen in FIGS. 9Aand 9B, the MSE due to these distortions remains below −20 dB whenshrinking the SRS bandwidth by 10%. The rest of the description of thesesimulations only considers the channel estimation performances inreduced shrunk bandwidth.

FIG. 9A illustrates a high error floor when 16 SRS users are multiplexedwith TU channel. This is due to the delay profile truncation. In thisconfiguration the cyclic shift increment is 4.17 μS but the delay spreadof the channel is 5 μS. It is not recommended to multiplex 16 UEs withTU channel on the same SRS symbol at high SNR.

Channel Estimator Performance with AWGN

The normalized mean square error performance σ_(H) ² is plotted in FIGS.10 and 11 for TU and PA channels when varying the number of multiplexedSRS users and the SRS bandwidth respectively. FIGS. 10A and 10Billustrates plots of Channel estimation Mean Squared Error in ChannelQuality Indicator (CQI) estimates of the shrunk bandwidth in dB versussignal to noise ratio (SNR) in dB. FIG. 10A is the TU channel. FIG. 10Bis the PA channel. FIGS. 10A and 10B illustrate four curves: two SRSusers; four SRS users; eight SRS users; and sixteen SRS users. Asdescribed above an error floor occurs with 16 SRS users with TU channel(FIG. 10A) because of the delay profile truncation. The better channelestimation performance with PA channel compared to TU channel is due tothe slower channel variations in frequency domain. This provides betterinterpolation performance and, due to the smaller the delay spread, thelarger the SNR improvement ratio described above. FIG. 10B illustratesthe smaller the SRS bandwidth the narrower the low-pass filter effectdiscussed above. The TU channel is more sensitive to the SRS bandwidththan PA channel because it is more frequency selective and thereforesuffers more from these losses.

Non-Biased Estimator

A broad use of the SRS allows prediction of the UE's signal tointerference plus noise ratio (SINR) information for the UL scheduler toderive appropriate scheduling metric and perform link adaptation. Thisinvolves computing the channel gain estimate per sub-carrier perantenna:

{circumflex over (G)}(a)=|{circumflex over (H)}(a)|²  (10)

In absence of other distortion but AWGN, channel estimatesĤ(a)=Ĥ_(x)(a)+jĤ_(y)(a) are complex values random variables whichcomponents follow a non-centered Normal distribution:

$\begin{matrix}{{{{{\hat{H}}_{x}(a)} = {a_{x}{N\left( {1,\frac{\sigma_{H}^{2}}{2}} \right)}}};}{{{{\hat{H}}_{y}(a)} = {a_{y}{N\left( {1,\frac{\sigma_{H}^{2}}{2}} \right)}}};}{{a_{x}^{2} + a_{y}^{2}} = a^{2}}} & (11)\end{matrix}$

As a result, the channel gain estimatesĜ(a)=|Ĥ(a)|²=|Ĥ_(x)(a)|²+|Ĥ_(y)(a)|² follow a non-central Chi-squaredistribution with 2 degrees of freedom and non-centrality parameter a².The normalized mean and standard deviations are:

$\begin{matrix}{\frac{m_{\hat{G}{(a)}}}{a^{2}} = {1 + \sigma_{H}^{2}}} & (12) \\{\frac{\sigma_{\hat{G}{(a)}}}{a^{2}} = {\sigma_{H}\sqrt{2 + \sigma_{H}^{2}}}} & (13)\end{matrix}$

From equation (12) it is clear that this estimator is biased and thatthe noise variance component a²σ_(H) ² should be removed from the gainestimate Ĝ(a) to produce a non-biased estimation:

Ĝ ₀(a)=|{circumflex over (H)}(a)|²−{circumflex over (σ)}_(N) ²  (14)

where: {circumflex over (σ)}_(N) ² is an estimate of the noise varianceσ_(N) ²=a²σ_(H) ². However, |Ĥ(a)|² and {circumflex over (σ)}_(N) ² areindependent estimates which cumulative errors may lead to a negativevalue for Ĝ₀(a). Therefore some additional adjustment is needed toprevent negative gain estimates. Three possible options are:

$\begin{matrix}{{{\hat{G}}_{Abs}(a)} = {{{{\hat{H}(a)}}^{2} - {\hat{\sigma}}_{N}^{2}}}} & (15) \\{{{\hat{G}}_{Clip}(a)} = {\max \left\{ {{{{\hat{H}(a)}}^{2} - {\hat{\sigma}}_{N}^{2}};G_{floor}} \right\}}} & (16) \\{{{\hat{G}}_{Select}(a)} = \left\{ \begin{matrix}{{{\hat{H}(a)}}^{2} - {\hat{\sigma}}_{N}^{2}} & {{{{if}\mspace{14mu} {{\hat{H}(a)}}^{2}} - {\hat{\sigma}}_{N}^{2}} > 0} \\{{\hat{H}(a)}}^{2} & {{{{if}\mspace{14mu} {{\hat{H}(a)}}^{2}} - {\hat{\sigma}}_{N}^{2}} \leq 0}\end{matrix} \right.} & (17)\end{matrix}$

The comparative performance analysis of the above channel gain estimatesis discussed below.

Noise Variance Estimation Through Cyclic Shift Reservation

The variance of the SRS noise is specific to the SRS signal. The SRSsignal in addition to the thermal noise is expected to be interfered byother SRS signals from neighbor cells. This is reflected by thecross-correlation characteristics of EZC sequences. The noise variancecan be estimated from the areas where no signal energy is present in theconcatenated delay profiles sequence y. For some channel types such asTU and when all multiplexing space is used, there is no such areaavailable for noise variance estimation. In this invention one cyclicshift per comb is reserved for noise variance estimation. FIG. 12 showsthis technique. FIG. 12 shows a plot of power delay profile versus timesamples. Time samples 1 to 30 are reserved for user 1. Time samples 31to 60 are reserved for user 2. Time samples 61 to are reserved for user3. Time samples 91 to 120 are reserved for cyclic shift noiseestimation. As illustrated in FIG. 12, the noise estimation window isdesigned to maximize the number of noise samples while not includingsamples carrying adjacent users' energy such as in the spill-overregions. The noise is estimated as:

$\begin{matrix}{{\hat{\sigma}}_{N}^{2} = {\frac{1}{I_{N}}{\sum\limits_{i \in I_{N}}{y_{i}}^{2}}}} & (18)\end{matrix}$

where: I_(N) is the noise estimation window; and |I_(N)| is the numberof samples in this window.

Noise Variance Estimation Performance

Simulations of the normalized mean error (bias) m_(σ) _(N) ₂ andnormalized standard deviation σ_(σ) _(N) ₂ performance metrics for thenoise variance estimator result in the following:

m _(σ) _(N) ₂ =E{{circumflex over (σ)} _(N) ²−σ_(N) ²}/σ_(N) ²  (19)

σ_(σ) _(N) ₂ =√{square root over (E{([{circumflex over (σ)}_(N) ²−σ_(N)²]/σ_(N) ² −m _(σ) _(N) ₂ )²})}  (20)

FIG. 13 shows the noise variance estimation performance for both TU andPA channels when varying the number of SRS users at 20 PRB SRSbandwidth. FIG. 13 illustrates plots of noise power estimationperformance versus signal to noise ratio in dB for both the TU channeland the PA channel. FIG. 13A illustrates the mean error and FIG. 13Billustrates the standard deviation of the error. The mean errorperformance shows the noise power estimator is unbiased in the areawhere it is the most important: at low SNR of less than 0 dB. At highSNR, the estimator has a non-zero mean due to non-ideal cyclic shiftseparation between users and noise window. The standard deviationperformance shows the noise power estimator has a constant variance inthe area where it is the most important: at low SNR less than 0 dB. Athigh SNR, the estimator variance increases with SNR due to non-idealcyclic shift separation between users and noise window. The PA channelprovides a more accurate estimation because the noise estimation windowcan be made larger thanks to the small delay spread of adjacent UEs asshown in FIG. 10.Channel Gain Estimator Performance with AWGN

To determine if the modified channel gain estimator Ĝ₀(a) is unbiased,simulations measure the normalized linear mean error (bias) m_(H) ₂defined as:

$\begin{matrix}{m_{H^{2}} = \frac{E\left\{ {{{\hat{G}}_{0}(a)} - {{H(a)}}^{2}} \right\}}{a^{2}}} & (21)\end{matrix}$

FIG. 14 shows the channel gain estimation error with and without noisevariance estimation removal for both the TU channel (FIG. 14A) and thePA channel (FIG. 14B) for varying the number of SRS users at 20 PRB SRSbandwidth. FIG. 14 is two plots of channel gain estimation error versussignal to noise ratio in dB for with no noise removal and with noiseremoval. The channel gain estimator Ĝ₀(a) is not biased across the wideSNR range after removing the estimated noise variance.

The link-level simulator allows assessment of performance of thepositive channel gain estimators. Because the channel gain is furtherused for SNR estimation, it is more convenient to express it in the dBscale. The mean m_(H) ₂ _(dB) and standard deviation σ_(H) ₂ _(dB)errors of the channel gain estimations expressed in dB are:

m _(H) ₂ _(dB) =E{Ĝ _(xy)(a)_(dB)−(|H(a)|²)_(dB)}  (19)

σ_(H) ₂ _(dB)=√{square root over (E{(Ĝ _(xy)(a)−(|H(a)|²)_(dB) −m _(H) ₂_(dB))²})}  (20)

where: Ĝ_(xy)(a) represent the various estimators Ĝ_(Abs)(a),Ĝ_(Clip)(a) and Ĝ_(Select)(a). FIG. 15 illustrates the mean channel gainestimation error (FIG. 15A) and standard deviation of the channel gainestimation error (FIG. 15B) versus signal to noise ratio in dB forvarious gain estimation techniques for the TU channel. FIG. 15 includescurves for: no noise removal; calculation using absolute value;selective calculation; clipping the channel gain estimation at −20 dB;clipping the channel gain estimation at −23 dB; and clipping the channelgain estimation at −30 dB. FIGS. 15A and 15B each employ 2 SRS users.FIG. 16 illustrates the mean channel gain estimation error (FIG. 16A)and standard deviation of the channel gain estimation error (FIG. 16B)versus signal to noise ratio in dB for various gain estimationtechniques for the PA channel. FIG. 16 includes curves for: no noiseremoval; calculation using absolute value; selective calculation;clipping the channel gain estimation at −20 dB; clipping the channelgain estimation at −23 dB; and clipping the channel gain estimation at−30 dB. FIGS. 15A and 15B each employ 2 SRS users. The methods providingthe best compromise across both mean and standard deviation errors andacross the SNR range are the clipping methods with clipping threshold of−20 dB or −23 dB.

Further Noise Reduction Techniques

Both channel and channel gain estimators performances show rather poorperformances at low SNR. This section of the patent applicationevaluates ways to improve these performances through two noise reductiontechniques. The resulting performances on both the TU channel and the PAchannel are assessed. This simulation used an SRS configuration withonly 2 SRS users per SRS symbol (minimum co-channel interference) and 20PRB SRS bandwidth in order to isolate the noise reduction performance.The channel gain estimator in dB scale used a clipping threshold of −20dB for negative gain avoidance.

Least Mean Square (LMS) Filtering

The least mean square filtering method implements an LMS equalizer onthe channel estimates Ĥ_(u) before computing the channel gain:

Ĥ _(eq) =C _(LMS) Ĥ _(u)  (24)

where: C_(LMS) is the N_(SRS) by N_(SRS) coefficient matrix minimizingthe mean square error (MSE) and computed as:

C _(LMS)=Γ⁻¹ξ  (25)

where: Γ is the covariance matrix of the sub-carrier samples and; ξ is amatrix which columns are shifted replicas of the frequency domainchannel filter coefficients. In the link-level simulator, both Γ and ξare selected according to the channel model in use. In a practical eNBimplementation different UEs may undergo different channels. Thus it canbe quite complex to track the channel delay and amplitude profile ofeach UE independently. This patent application uses only the maximumdelay spread information from the channel model and scaled a sincfunction accordingly to model both Γ and ξ resulting in a common set ofcoefficients C_(LMS) for all SRS users. FIGS. 17 and 18 compare theperformance of the channel estimators with and without LMS filtering forboth the TU channel and the PA channel. FIG. 17 plots the normalized MSEperformance mean square error σ_(H) ² of the channel estimates Ĥ persub-carrier per antenna in dB versus signal to noise ratio in dB for twoSRS users. FIG. 17 includes four curves: TU channel with least meansquare (LMS) filtering disabled; TU channel with LMS filtering enabled;PA channel with LMS filtering disabled; and PA channel with LMSfiltering enabled. At low SNR, the LMS filter reduces the MSE by up to 3dB for both PA and TU channels. For the TU channel, the LMS filtercreates an error floor for positive SNR values.

FIG. 18 is two plots of channel gain estimation mean error (FIG. 18A)and channel gain estimation standard deviation of error (FIG. 18B)versus signal to noise ratio in dB for systems with two SRS users. Eachof FIGS. 18A and 18B illustrate four curves: TU channel with LMSfiltering disabled; TU channel with LMS filtering enabled; PA channelwith LMS filtering disabled; and PA channel with LMS filtering enabled.For the MSE performance (FIG. 18A), the LMS filter improves the meanerror by 2 and 1.2 dB for TU and PA channel respectively at low SNR andimproves the standard deviation performance (FIG. 18B) by 1 and 0.5 dBfor TU and PA channel respectively. For the TU channel the LMS filtercreates an error floor for positive SNR values. There is an SNRthreshold for each channel where a crossover occurs between LMSfiltering and no LMS filtering. Thus LMS filtering should be only usedbelow these thresholds:

TU channel: <0 dB; and

PA channel: <10 dB

Cyclic Shift Window Shrink

Another noise reduction technique shrinks the cyclic shift window n₁(u),. . . , n_(L)(u) when de-multiplexing the user thus reducing the valueof L. Since L is dimensioned to cope with the maximum expected delayspread of the user, reducing L creates a trade-off between the resultingchannel estimation distortion and the achieved noise reduction. FIGS. 19and 20 compare the performance of the channel estimators for variousamounts of shrinks for both the TU channel and the PA channel. FIG. 19plots the normalized MSE performance σ_(H) ² of the channel estimates Ĥversus signal to noise ratio per sub-carrier per antenna for variouswindow shrink amounts. FIG. 19A is for the TU channel. FIG. 19B is forthe PA channel. FIGS. 19A and 19B each show four curves: window shrink0%; window shrink 40%; window shrink 60%; and window shrink 80%.Different shrink amounts provide optimal noise reduction in differentSNR regions. This is summarized in Table 4.

TABLE 4 SNR CHANNEL MODEL region TU PA (dB) [−20 −8] ]−8 −5] ]−5 0] ]020] ]−20 −10] ]−10 0] ]0 8] ]8 20] Cyclic shift 80% 60% 40% 0% 80% 60%40% 0% window shrinkGiven the SNR regions are different for the TU channel and the PAchannel, this requires that eNB tracks both the SNR and the channelprofile, or at least the delay spread of each SRS user. At low SNR,shrinking the cyclic shift window by up to 80% reduces the MSE by up to6 dB for both PA and TU channels.

FIG. 20 illustrates plots of the mean errors of the channel gainestimator versus signal to noise ratio in dB. FIG. 20A is for the TUchannel. FIG. 20B is for the PA channel. FIGS. 20A and 20B each showfour curves: window shrink 0%; window shrink 40%; window shrink 60%; andwindow shrink 80%. FIG. 21 illustrates plots of the standard deviationof the channel gain estimator versus signal to noise ratio in dB. FIG.21A is for the TU channel. FIG. 21B is for the PA channel. FIGS. 21A and21B each show four curves: window shrink 0%; window shrink 40%; windowshrink 60%; and window shrink 80%. For MSE performance (FIG. 20) a 80%cyclic shift window shrink improves at low SNR the mean error by up to2.1 and 2.5 dB for respective TU channel and PA channel. A 80% cyclicshift window shrink improves the standard deviation (FIG. 21) by 1 and1.2 dB for respective TU channel and PA channel.

This method provides the benefit of low complexity but is sensitive tothe granularity of the time samples n₁(u), . . . , n_(L)(u) of theuser's delay profile, the SRS bandwidth. It is clear from Table 1 thatsome SRS bandwidth configurations lead to such small number L of samplesin the cyclic shift window that shrinking further this value will leadto more distortion errors. FIGS. 21, 22 and 23 check the impact of theSRS bandwidth (4, 8 and 20 PRBs) on the cyclic shift window shrinkperformance. FIG. 21 illustrates plots of the standard deviation in thechannel gain estimator error versus signal to noise ratio in dB. FIG.21A is for the TU channel. FIG. 21B is for the PA channel. FIGS. 21A and21B each show four curves: window shrink 0%; window shrink 40%; windowshrink 60%; and window shrink 80%. FIG. 22 illustrates plots of the meansquare error in channel estimate error versus signal to noise ratio forvarious conditions. FIG. 22A includes six curves for a window shrink of80%: TU channel with an SRS bandwidth of 20 PRBs; TU channel with an SRSbandwidth of 8 PRBs; TU channel with an SRS bandwidth of 4 PRBs; PAchannel with an SRS bandwidth of 20 PRBs; PA channel with an SRSbandwidth of 8 PRBs; and PA channel with an SRS bandwidth of 4 PRBs.FIG. 22B includes 4 curves for a SRS bandwidth of 4 PRBs: TU channelwith a window shrink of 0%; TU channel with a window shrink of 80%; PAchannel with a window shrink of 0%; and PA channel with a window shrinkof 80%. FIG. 23 illustrates plots of the standard deviation in channelestimate error versus signal to noise ratio for various conditions. FIG.23A includes six curves for a window shrink of 80%: TU channel with anSRS bandwidth of 20 PRBs; TU channel with an SRS bandwidth of 8 PRBs; TUchannel with an SRS bandwidth of 4 PRBs; PA channel with an SRSbandwidth of 20 PRBs; PA channel with an SRS bandwidth of 8 PRBs; and PAchannel with an SRS bandwidth of 4 PRBs. FIG. 23B includes 4 curves fora SRS bandwidth of 4 PRBs: TU channel with a window shrink of 0%; TUchannel with a window shrink of 80%; PA channel with a window shrink of0%; and PA channel with a window shrink of 80%. As can be seen fromFIGS. 21A, 22A and 23A where an 80% shrink is applied, at low SNR whereit is the most useful, the SRS bandwidth has negligible impact on thenoise reduction performance for the TU channel. It is more important forPA channel due to already small cyclic shift window (Table 3). At 4 PRBSRS bandwidth (FIGS. 21B, 22B and 23B) the low end SNR PA channelperformance is degraded to such extend that it becomes aligned with theTU channel performance. This should be compared though with the PRB SRSperformance without cyclic shift window shrink. FIGS. 21B, 22B and 23Bshow the noise reduction gain resulting from 80% cyclic shift windowshrink is preserved, compared to that achieved with 20 PRB SRS. Thusthere is better performance in the PA channel with smaller bandwidths athigh SNR. This is due to the very limited channel variation of PA acrosssuch small bandwidths. Therefore, the per-subcarrier channel estimationmatches more easily the actual channel.

Shrinking the cyclic shift window makes the estimator less robust totiming errors perhaps requiring compensating them before channelestimation. FIGS. 25 and 26 illustrate the impact of a ±0.5 μS timingerror on the channel and channel gain estimation performances on theworst-case configuration for this noise reduction technique. FIG. 25illustrates mean square error of channel estimates for 4-PRB SRSbandwidth and 80% cyclic shift window shrink versus signal to noiseratio. FIG. 25 includes four curves: TU channel with no timing error; TUchannel with ±0.5 μS timing error; PA channel with no timing error; andPA channel with ±0.5 μS timing error. FIG. 26 illustrates channel gainestimation mean error (FIG. 26A) and standard deviation channel gainestimation error (FIG. 26B) versus signal to noise ratio. FIGS. 26A and26B each include four curves: TU channel with no timing error; TUchannel with ±0.5 μS timing error; PA channel with no timing error; andPA channel with ±0.5 μS timing error. As shown in FIGS. 25 and 26 for a±0.5 μS timing error the granularity of the TA command is expected to bethe maximum residual timing error from the closed-loop UL timingsynchronization procedure. At low SNR where it is the most useful (lessthan −10 dB, see Table 5) the timing errors have negligible impact onthe noise reduction performance for both the TU channel and the PAchannel.

Combined Cyclic Shift Window Shrink and LMS Filtering

FIGS. 27 and 28 illustrate whether both noise reduction techniques gainscould be cumulated. FIGS. 27 and 28 provide channel estimationperformances when an 80% shrink is applied to the cyclic shift window.FIG. 27 illustrates plots of mean square error in channel estimationversus signal to noise ratio with and without least mean squaredfiltering. FIG. 27 illustrates four curves: TU channel without LMSfiltering; TU channel with LMS filtering; PA channel without LMSfiltering; and PA channel with LMS filtering. FIG. 28 illustrates themean channel gain estimation error (FIG. 28A) and standard deviation ofthe channel gain estimation error (FIG. 28B) versus signal to noiseratio in dB for various LMS techniques for the TU channel and the PAchannel. FIG. 16 includes curves for: TU channel without LMS filtering;TU channel with LMS filtering; PA channel without LMS filtering; and PAchannel with LMS filtering. FIGS. 27 and 28 illustrate that enabling ordisabling LMS equalization on top does not have any impact onperformance. Thus these two techniques are not cumulative and should beused separately.

Noise Reduction Techniques Summary

FIGS. 27 and 28 show that noise reduction techniques should be usedselectively depending on the SNR region. Some rough a-priori knowledgeof the UE geometry should be assumed. This knowledge can be derived fromeither long term SNR tracking for each UE or preliminary instantaneousSNR estimation. Given the higher complexity of the latter optionrequiring multiple channel estimation steps (preliminary, final), theformer approach is preferrable. The SNR regions boundaries are channelor delay spread specific. The eNB should track each user's delay spreadfor this purpose. Table 5 summarizes the performance comparison betweenboth noise reduction techniques and shows that the cyclic shift windowshrink outperforms the LMS filtering. From a complexity view point, theLMS filter is also more costly. This makes the cyclic shift windowshrink the best option for noise reduction.

TABLE 5 NOISE REDUCTION TECHNIQUE LMS CYCLIC SHIFT WINDOW FILTERINGSHRINK Channel Model TU PA TU PA Channel estimation MSE 3 dB  3 dB 6 dB 6 dB Channel gain mean error 2 dB 1.2 dB 2.1 dB  2.5 dB Channel gainstandard 1 dB 0.5 dB 1 dB 1.2 dB deviation

Channel and Channel Gain Estimation Summary

FIGS. 29 to 31 provide a comprehensive set of channel and channel gainperformance plots with TU and PA channels for varying numbers of SRSusers and the bandwidth. Since one cyclic shift is reserved for noisevariance estimation for each SRS comb, the remaining number ofmultiplexed users per SRS symbol is 2, 3 and 14 with 2, 4 and 8 cyclicshifts per comb respectively. FIG. 29 illustrates the mean square errorof channel estimation versus signal to noise ratio for various number ofSRS users for 20-PRB SRS bandwidth (FIG. 29A) and for 6 TU channel usersand 14 PA channel users (FIG. 29B). FIG. 29A has six curves: TU channeland 2 SRS users; TU channel and 6 SRS users; TU channel and 14 SRSusers; PA channel and 2 SRS users; PA channel and 6 SRS users; PAchannel and 14 SRS users. FIG. 29B has 6 curves: TU channel with an SRSbandwidth of 20 PRBs; TU channel with an SRS bandwidth of 8 PRBs; TUchannel with an SRS bandwidth of 4 PRBs; PA channel with an SRSbandwidth of 20 PRBs; PA channel with an SRS bandwidth of 8 PRBs; and PAchannel with an SRS bandwidth of 4 PRBs. FIG. 30 illustrates the channelgain estimation mean error versus signal to noise ratio for variousnumber of SRS users for 20-PRB SRS bandwidth (FIG. 30A) and for 6 TUchannel users and 14 PA channel users (FIG. 30B). FIG. 30A has sixcurves: TU channel and 2 SRS users; TU channel and 6 SRS users; TUchannel and 14 SRS users; PA channel and 2 SRS users; PA channel and 6SRS users; PA channel and 14 SRS users. FIG. 30B has 6 curves: TUchannel with an SRS bandwidth of 20 PRBs; TU channel with an SRSbandwidth of 8 PRBs; TU channel with an SRS bandwidth of 4 PRBs; PAchannel with an SRS bandwidth of 20 PRBs; PA channel with an SRSbandwidth of 8 PRBs; and PA channel with an SRS bandwidth of 4 PRBs.FIG. 31 illustrates the channel gain estimation standard deviationversus signal to noise ratio for various number of SRS users for 20-PRBSRS bandwidth (FIG. 31A) and for 6 TU channel users and 14 PA channelusers (FIG. 31B). FIG. 31A has six curves: TU channel and 2 SRS users;TU channel and 6 SRS users; TU channel and 14 SRS users; PA channel and2 SRS users; PA channel and 6 SRS users; PA channel and 14 SRS users.FIG. 31B has 6 curves: TU channel with an SRS bandwidth of 20 PRBs; TUchannel with an SRS bandwidth of 8 PRBs; TU channel with an SRSbandwidth of 4 PRBs; PA channel with an SRS bandwidth of 20 PRBs; PAchannel with an SRS bandwidth of 8 PRBs; and PA channel with an SRSbandwidth of 4 PRBs. This assumes that: noise reduction from cyclicshift window truncation with SNR-based selective truncation is accordingto Table 4; and the Channel gain estimator in dB scale, with a clippingthreshold G_(floor) of −20 dB for negative gain avoidance.

FIGS. 29 to 31 show that TU channel error floors occur with 14 SRS usersor at small bandwidth. This is due to truncated delay spread (14 SRSusers) or channel band-pass filtering at small bandwidth due to downsampling at de-mapping/IDFT stage. With the PA channel, the delay spreadis small enough to prevent from strong co-cyclic-shift interference,even with 16 users per symbol and down to 4-PRB bandwidth.

SNR Estimation

This section studies the impact of both noise and channel gainestimators previously described on the signal over noise ratio (SNR)estimation in support of a scheduler. In the current description thefocus is upon the SNR. The simulations modeled the thermal noisecomponent. It is expected that interference from SRS users in othercells reflects the good cross-correlation characteristics of EZCsequences which can be approximated as Gaussian noise at first order.

SNR Expressions

The per sub-carrier SNR vector ρ_(sc,p) experienced at eNB antenna portp is expressed as:

$\begin{matrix}{\rho_{{sc},p} = \frac{H_{p}^{2}(a)}{\sigma_{N}^{2}}} & (26)\end{matrix}$

where: H_(p) ²(a) is an N_(SRS) size vector reflecting the channel gainexperienced on antenna port p on the N_(SRS) sub-carriers; a² is theaveraged received power from the SRS user; and σ_(N) ² is the varianceof the AWGN sub-carriers samples. This SNR is then combined acrossantennas to provide the “MRC'ed” per sub-carrier SNR vector

ρ_(sc) = (ρ_(f₁), ρ_(f₂), …  , ρ_(f_(N_(SRS))))^(T)

as:

$\begin{matrix}{\rho_{sc} = {\sum\limits_{p = 1}^{A}\rho_{{sc},p}}} & (27)\end{matrix}$

where: A is the number of receive antennas; and f₁, f₂, . . . , f_(N)_(SRS) are the sub-carriers allocated to the SRS.

Practical MAC schedulers use larger than per-subcarrier SINR frequencygranularity corresponding to the minimum frequency band of a user'sallocation, referred to as scheduling, and defined in integer numberN_(RB) of PRBs. There are typically two methods for SINR computationdepending on what type of scheduling unit scheduler supports: a fixedscheduling unit size, referred to as Fixed Transmission Bandwidth (FTB);or a variable scheduling unit size, referred to as Adaptive TransmissionBandwidth (ATB). For FTB, SINR is directly computed from per-subcarrierto per scheduling unit (1-step). ATB typically addresses RecursiveMaximum Expansion (RME) scheduling algorithms where different winnerscan have different allocation sizes depending on the scheduling metricenvelope shape. The envelope is computed with per-PRB granularity forthe simplest RME algorithm. This results in computing the remainingaveraging across PRBs only for the winners. In both cases, theshort-term SINR per scheduling unit is computed by averaging ρ_(sc)across the sub-carriers of the same scheduling unit, thus providing perscheduling unit effective SNR vector

ρ_(eff − su) = (ρ_(eff, s₁), ρ_(eff, s₂), …  , ρ_(eff, s_(M_(SRS))))^(T)

where; s₁, s₂, . . . , s_(M) _(SRS) are the

$M_{SRS} = \left\lfloor \frac{2N_{SRS}}{N_{sc}^{RB}N_{RB}} \right\rfloor$

scheduling units in the SRS allocation. The averaging method depends onthe OFDM access scheme and the type of equalizer used at the physicallayer.

With the single carrier property of the UL transmission and when ZFequalization is implemented at the L1 receiver the effective SINRρ_(eff,s) ^(ZF) across the N_(sc) ^(RB)N_(RB)/2 consecutive sub-carriersof a scheduling unit s is computed as:

$\begin{matrix}{\rho_{{eff},s}^{ZF} = \left( {\frac{2}{N_{sc}^{RB}N_{RB}}{\sum\limits_{f = {{sN}_{sc}^{RB}{N_{RB}/2}}}^{{({s + 1})}N_{sc}^{RB}{N_{RB}/2}}\frac{1}{\rho_{f}}}} \right)^{- 1}} & (28)\end{matrix}$

With the same transmission scheme but with MMSE equalization at thereceiver, the effective SINR ρ_(eff,s) ^(MMSE) is computed throughharmonic averaging as:

$\begin{matrix}\begin{matrix}{\rho_{{eff},s}^{MMSE} = \left\lbrack {\left( {\frac{2}{N_{sc}^{RB}N_{RB}}{\sum\limits_{f = {{sN}_{sc}^{RB}{N_{RB}/2}}}^{{({s + 1})}N_{sc}^{RB}{N_{RB}/2}}\frac{\rho_{f}}{1 + \rho_{f}}}} \right)^{- 1} - 1} \right\rbrack^{- 1}} \\{= {\left( {\frac{2}{N_{sc}^{RB}N_{RB}}{\sum\limits_{f = {{sN}_{sc}^{RB}{N_{RB}/2}}}^{{({s + 1})}N_{sc}^{RB}{N_{RB}/2}}\frac{1}{1 + \rho_{f}}}} \right)^{- 1} - 1}}\end{matrix} & (29)\end{matrix}$

Given MMSE is the most popular receiver for SC-FDMA, this invention onlyconsiders ρ_(eff,s) ^(MMSE).

Performance of SNR Estimators

The performance of the per-subcarrier SNR estimators {circumflex over(ρ)}_(sc-gen,p) and {circumflex over (ρ)}_(sc,p) with genie-aided andreal AWGN variance estimation are respectively:

$\begin{matrix}\left\{ \begin{matrix}{{{\hat{\rho}}_{{{sc}\text{-}{gen}},p} = \frac{{\hat{H}}_{p}^{2}(a)}{\sigma_{N}^{2}}};} & {{\hat{\rho}}_{{sc}\text{-}{gen}} = {\sum\limits_{p = 1}^{A}{\hat{\rho}}_{{{sc}\text{-}{gen}},p}}} \\{{{\hat{\rho}}_{{sc},p} = \frac{{\hat{H}}_{p}^{2}(a)}{{\hat{\sigma}}_{N}^{2}}};} & {{\hat{\rho}}_{sc} = {\sum\limits_{p = 1}^{A}{\hat{\rho}}_{{sc},p}}}\end{matrix} \right. & (30)\end{matrix}$

The channel gain estimate Ĥ_(p) ²(a) is given by Equation (16) with aclipping threshold G_(floor) of −20 dB for negative gain avoidance andnoise reduction from cyclic shift window truncation with selectivetruncation according to Table 4. Noise variance estimate {circumflexover (σ)}_(N) ² is given by Equation (18). In simulations the measuredmean (bias) and centered standard deviation performance of the aboveestimators, expressed in dB are:

$\begin{matrix}\left\{ \begin{matrix}{{m_{\rho_{{sc}\text{-}{genp}}} = {E\left\{ {\left( {\hat{\rho}}_{{sc}\text{-}{genp}} \right)_{dB} - \left( \rho_{{sc}\text{-}{genp}} \right)_{dB}} \right\}}};} & {\sigma_{\rho_{{sc}\text{-}{genp}}} = \sqrt{E\left\{ \begin{bmatrix}{\left( {\hat{\rho}}_{{sc}\text{-}{genp}} \right)_{dB} -} \\{\left( \rho_{{sc}\text{-}{genp}} \right)_{dB} -} \\m_{\rho_{{sc}\text{-}{genp}}}^{2}\end{bmatrix}^{2} \right\}}} \\{{m_{\rho_{{sc}\text{-}{gen}}} = {E\left\{ {\left( {\hat{\rho}}_{{sc}\text{-}{gen}} \right)_{dB} - \left( \rho_{{sc}\text{-}{gen}} \right)_{dB}} \right\}}};} & {\sigma_{\rho_{{sc}\text{-}{gen}}} = \sqrt{E\left\{ \begin{bmatrix}{\left( {\hat{\rho}}_{{sc}\text{-}{gen}} \right)_{dB} -} \\{\left( \rho_{{sc}\text{-}{gen}} \right)_{dB} -} \\m_{\rho_{{sc}\text{-}{gen}}}^{2}\end{bmatrix}^{2} \right\}}} \\{{m_{\rho_{{sc},p}} = {E\left\{ {\left( {\hat{\rho}}_{{sc},p} \right)_{dB} - \left( \rho_{{sc},p} \right)_{dB}} \right\}}};} & {\sigma_{\rho_{{sc},p}} = \sqrt{E\left\{ \begin{bmatrix}{\left( {\hat{\rho}}_{{sc},p} \right)_{dB} -} \\{\left( \rho_{{sc},p} \right)_{dB} -} \\m_{\rho_{{sc},p}}^{2}\end{bmatrix}^{2} \right\}}} \\{{m_{\rho_{sc}} = {E\left\{ {\left( {\hat{\rho}}_{sc} \right)_{dB} - \left( \rho_{sc} \right)_{dB}} \right\}}};} & {\sigma_{\rho_{sc}} = \sqrt{E\left\{ \begin{bmatrix}{\left( {\hat{\rho}}_{sc} \right)_{dB} -} \\{\left( \rho_{sc} \right)_{dB} -} \\m_{\rho_{sc}}^{2}\end{bmatrix}^{2} \right\}}}\end{matrix} \right. & (31)\end{matrix}$

FIG. 32 shows the per-subcarrier SNR estimators performance for both TUand PA channels for 20-PRB SRS bandwidth and when running 2 SRS usersper symbol. FIG. 32 shows mean signal to noise error (FIG. 32A) andstandard deviation of the signal to noise error (FIG. 32B) versus signalto noise ratio for various conditions with 20 PRB SRS bandwidth and 2SRS users per symbol. FIGS. 32A and 32B each show eight curves: TUchannel SNR per antenna with exact noise; TU channel SNR per antennawith estimated noise; TU channel SNR combined with exact noise; TUchannel SNR combined with estimated noise; PA channel SNR per antennawith exact noise; PA channel SNR per antenna with estimated noise; PAchannel SNR combined with exact noise; and PA channel SNR combined withestimated noise.

FIG. 32 shows that for low SNR, the per-antenna SNR estimationperformance is very much in line with the channel gain performance. Thisconfirms the good performance of the noise variance estimator. At highSNR, the noise variance estimate bias and large standard deviation dueto co-channel interference creates both a bias and a standard deviationrise on the SNR estimates. The SNR estimation in support of a schedulerwill rather use noise and interference estimation from the DMRS ratherthan the SRS. This is because it is more representative of the noise andinterference experienced by PUSCH. Therefore, this is not a major issueand this invention uses ideal noise estimates in the following SNRperformance investigations.

The expected SNR estimation standard deviation improvement whencombining the estimates across antennas is 2 to 2.5 dB.

The performance of the per-chunk SNR estimators {circumflex over(ρ)}_(ch-H) and {circumflex over (ρ)}_(ch-A) with harmonic andarithmetic averaging is respectively:

$\begin{matrix}{{\hat{\rho}}_{{ch}\text{-}H} = {\left( {\frac{2}{N_{sc}^{RB}N_{RB}}{\sum\limits_{f = {{sN}_{sc}^{RB}{N_{RB}/2}}}^{{({s + 1})}N_{sc}^{RB}{N_{RB}/2}}\frac{1}{1 + {\rho_{{sc}\text{-}{gen}}(f)}}}} \right)^{- 1} - 1}} & (32) \\{{\hat{\rho}}_{{ch}\text{-}A} = {\frac{2}{N_{sc}^{RB}N_{RB}}{\sum\limits_{f = {{sN}_{sc}^{RB}{N_{RB}/2}}}^{{({s + 1})}N_{sc}^{RB}{N_{RB}/2}}{\rho_{{sc}\text{-}{gen}}(f)}}}} & (33)\end{matrix}$

From simulations the mean (bias) and centered standard deviationperformance of the above estimators, expressed in dB is:

$\quad\begin{matrix}\left\{ \begin{matrix}{{m_{{\hat{\rho}}_{{ch}\text{-}H}} = {E\left\{ {\left( {\hat{\rho}}_{{ch}\text{-}H} \right)_{dB} - \left( {\hat{\rho}}_{{ch}\text{-}H} \right)_{dB}} \right\}}};} & {\sigma_{\rho_{{ch}\text{-}H}} = \sqrt{E\left\{ \begin{bmatrix}{\left( {\hat{\rho}}_{{ch}\text{-}H} \right)_{dB} - \left( \rho_{{ch}\text{-}H} \right)_{dB} -} \\m_{\rho_{{ch}\text{-}H}}^{2}\end{bmatrix}^{2} \right\}}} \\{{m_{{\hat{\rho}}_{{ch}\text{-}A}} = {E\left\{ {\left( {\hat{\rho}}_{{ch}\text{-}A} \right)_{dB} - \left( {\hat{\rho}}_{{ch}\text{-}A} \right)_{dB}} \right\}}};} & {\sigma_{\rho_{{ch}\text{-}A}} = \sqrt{E\left\{ \begin{bmatrix}{\left( {\hat{\rho}}_{{ch}\text{-}A} \right)_{dB} - \left( \rho_{{ch}\text{-}H} \right)_{dB} -} \\m_{\rho_{{ch}\text{-}A}}^{2}\end{bmatrix}^{2} \right\}}}\end{matrix} \right. & (41)\end{matrix}$

FIGS. 33 and 34 show the per-chunk SNR estimators performance for boththe TU channel and the PA channels for 20-PRB SRS bandwidth and whenrunning 2 SRS users per symbol. FIG. 33 is the mean chuck SNR errorversus signal to noise ratio for various chunk averaging. FIG. 33A isthe TU channel. FIG. 33B is the PA channel. FIGS. 33A and 33B each havefour curves: 1 PRB chunk arithmetic averaging; 1 PRB chunk harmonicaveraging; 5 PRB chunk arithmetic averaging; and 5 PRB chunk harmonicaveraging. FIG. 34 is the standard deviation of the chunk SNR errorversus signal to noise ratio for various chunk averaging. FIG. 34A inthe TU channel. FIG. 34B is the PA channel. FIGS. 34A and 33B each havefour curves: 1 PRB chunk arithmetic averaging; 1 PRB chunk harmonicaveraging; 5 PRB chunk arithmetic averaging; and 5 PRB chunk harmonicaveraging.

FIGS. 33 and 34 illustrate that there is no difference betweenarithmetic and harmonic averaging on TU channel for UE geometry below −5dB and −10 dB for 1-PRB and 5-PRB respectively. There is no differenceat all either across the SNR range between arithmetic and harmonicaveraging on PA channel. This is due to the flat behavior of PA channelacross the averaged sub-carriers, in which case Equation (29) simplifiesto an arithmetic mean. At high SNR, arithmetic averaging of TU channelhas a bias error of 0.5 dB and 1.4 dB for 1-PRB and 5-PRB chunksrespectively as well as a worse standard deviation performance withrespect to harmonic averaging of 0.5 dB and 0.9 dB for 1-PRB and 5-PRBchunks respectively. Thus similarly to what was done for the channelgain estimation, harmonic or arithmetic averaging can be appliedselectively depending on the UE's SNR. As for the SNR-based selectivetruncation, some rough a-priori knowledge of the UE geometry can beassumed sufficient to map the UE in either of the two SNR regions(high/low SNR) as per the thresholds noted above. The benefit of this isthat the lower complexity arithmetic averaging can be used wheneverpossible.

FIGS. 33 and 34 also show the chunk-SNR estimation performance improveswith the chunk size as more averaging is performed.

Sub-Carrier Decimation

Another important complexity reduction comes from the sub-carrierdecimation that can be applied when computing per-chunk SNR. Theperformance loss when applying the three decimation factors possiblewith 6 SRS sub-carriers per PRB is expected as: 2, 3 and 6. In order tominimize the decimation error, the resulting decimated samples arecentered in the PRB, as illustrated in FIG. 35.

FIG. 36 shows the performance of the per-PRB SNR estimator {circumflexover (ρ)}_(ch-H) (chunk size=1 PRB) when sub-carrier decimation isapplied during the harmonic averaging, for 20-PRB SRS bandwidth and whenrunning 6 and 14 SRS users per symbol for both the TU channel and the PAchannel. FIG. 36A illustrates the mean chunk SNR error versus signal tonoise ratio for various conditions. FIG. 36B illustrates the standarddeviation of the chunk SNR error versus signal to noise ratio forvarious conditions. FIGS. 36A and 36B each have 8 curves: TU channelwith a sub-carrier decimation factor of 1; TU channel with a sub-carrierdecimation factor of 2; TU channel with a sub-carrier decimation factorof 3; TU channel with a sub-carrier decimation factor of 6; PA channelwith a sub-carrier decimation factor of 1; PA channel with a sub-carrierdecimation factor of 2; PA channel with a sub-carrier decimation factorof 3; and PA channel with a sub-carrier decimation factor of 6. FIG. 36shows that a decimation factor of 6 (only one sub-carrier per PRB)should be precluded with TU channel. In all other cases, the performancedegradation from decimation factors does not exceed 0.1 dB. Thussub-carrier decimation factors of up to 3 and 6 can be applied whencomputing per-PRB SNR with TU and PA channels respectively.

SNR Performance Summary

FIGS. 37 and 38 illustrate a comprehensive set of per-PRB SNR estimationperformance plots for the TU channel and the PA channel when varying thenumber of SRS users and the SRS bandwidth. FIG. 37 illustrates the meanchunk SNR error versus signal to noise ratio for various number of SRSusers for 20-PRB SRS bandwidth (FIG. 37A) and for 6 TU channel users and14 PA channel users (FIG. 37B). FIG. 37A has six curves: TU channel and2 SRS users; TU channel and 6 SRS users; TU channel and 14 SRS users; PAchannel and 2 SRS users; PA channel and 6 SRS users; PA channel and 14SRS users. FIG. 37B has 6 curves: TU channel with an SRS bandwidth of 20PRBs; TU channel with an SRS bandwidth of 8 PRBs; TU channel with an SRSbandwidth of 4 PRBs; PA channel with an SRS bandwidth of 20 PRBs; PAchannel with an SRS bandwidth of 8 PRBs; and PA channel with an SRSbandwidth of 4 PRBs. FIG. 38 illustrates the standard deviation of thechunk SNR error versus signal to noise ratio for various number of SRSusers for 20-PRB SRS bandwidth (FIG. 38A) and for 6 TU channel users and14 PA channel users (FIG. 38B). FIG. 38A has six curves: TU channel and2 SRS users; TU channel and 6 SRS users; TU channel and 14 SRS users; PAchannel and 2 SRS users; PA channel and 6 SRS users; PA channel and 14SRS users. FIG. 38B has 6 curves: TU channel with an SRS bandwidth of 20PRBs; TU channel with an SRS bandwidth of 8 PRBs; TU channel with an SRSbandwidth of 4 PRBs; PA channel with an SRS bandwidth of 20 PRBs; PAchannel with an SRS bandwidth of 8 PRBs; and PA channel with an SRSbandwidth of 4 PRBs. One cyclic shift is reserved for noise varianceestimation for each SRS comb. The remaining number of multiplexed usersper SRS symbol is 2, 6 and 14 with 2, 4 and 8 cyclic shifts per combrespectively. From the conclusions drawn in the previous sections, thefollowing estimators are assumed:

-   -   {circumflex over (ρ)}_(ch-H) with harmonic averaging on TU        channel for UEs beyond −5 dB SNR;    -   {circumflex over (ρ)}_(ch-A) with arithmetic averaging on other        UEs, and for PA channel;    -   Sub-carrier decimation of 3.

Timing Offset Estimation Impact of Timing Errors

It is worth understanding first the impact of timing errors on theestimations performed on the SRS and the resulting performance loss ofthe per-PRB SNR estimation, involving the channel gain estimation fromSRS. FIG. 39 illustrates that in presence of timing errors, the usercyclic shift window n₁(u), . . . , n_(L)(u) in Equation (4) and FIG. 7must be enlarged to account for the maximum expected timing uncertainty.FIG. 39 illustrates the case of four cyclic-shift multiplexed UEs perSRS comb with 5 μS delay spread TU channel. The top part of FIG. 39shows a plot of power delay profile versus time sample for four userwindows. The bottom part of FIG. 39 shows a plot of demultipelexed powerdelay profile versus the same time samples. The negative time offsetsamples are folded back at the end of the user window. In addition, fornarrow channels such as PA channel in FIG. 12, a timing uncertaintywindow as low as ±0.5 μS is already larger than the channel delayspread, which makes it impossible to implement cyclic shift windowshrink. This is not the case of TU channel for which we still retain thenoise reduction technique. FIG. 40 illustrates the performancedegradation of the per-PRB SNR estimation with no sub-carrierdecimation, in presence of timing errors, for 20-PRB SRS bandwidth andwhen running 6 and 14 SRS users per symbol for both the TU channel andthe PA channel. FIG. 40A is the mean chunk SNR error. FIG. 40B is thestandard deviation of the chunk SNR error. Both FIGS. 40A and 40Billustrate 6 curves: TU channel with a maximum timing error of ±0.0 μS;TU channel with a maximum timing error of ±0.5 μS; TU channel with amaximum timing error of ±1.0 μS; PA channel with a maximum timing errorof ±0.0 μS; PA channel with a maximum timing error of ±0.5 μS; PAchannel with a maximum timing error of ±1.0 μS. FIG. 40 illustrates thatthe degradation is the most severe for the PA channel, with up to 3 dBand 1.7 dB degradation at the low end SNR for the mean and standarddeviation respectively. This is because the noise reduction techniquebased on cyclic shift window shrink must be disabled with PA channel inpresence of non-compensated timing errors. For the TU channel, the noisereduction technique remains active and the performance loss due totiming errors is bounded by 1 dB and 1.5 dB for the mean and standarddeviation respectively. This is restricted to a small SNR region and ismainly due to the fact that the optimized shrink amounts and SNR regionsfrom Table 4 are not optimal after adjusting the user cyclic shiftwindow for timing errors as shown in FIG. 39 and should be tuned again.No significant difference is observed on both channels between a timinguncertainty window of ±0.5 μS and ±1.0 μS.

FIG. 41 illustrates the impact of narrowing the SRS bandwidth down to 4PRBs which further reduces the user cyclic shift window size, inpresence of timing errors of ±0.5 μS. FIG. 41 illustrates the mean chunkSNR error (FIG. 41A) and the standard deviation of the mean chunk SNRerror (FIG. 41B) for various SRS bandwidths for both the TU channel andthe PA channel. Both FIGS. 40A and 40B illustrate 6 curves: TU channelwith an SRS bandwidth of 20 PRBs; TU channel with an SRS bandwidth of 8PRBs; TU channel with an SRS bandwidth of 4 PRBs; PA channel with an SRSbandwidth of 20 PRBs; PA channel with an SRS bandwidth of 8 PRBs; and PAchannel with an SRS bandwidth of 4 PRBs. In the worst-case an additional0.5 dB loss can be seen in FIG. 41.

Timing Offset Estimation

One additional benefit of the time-domain based channel estimation isthat it allows implementing a simple timing offset estimator from theconcatenated delay profiles sequence y by combining the amplitude delayprofiles across antennas and searching for the highest peak in theuser's timing offset window:

$\begin{matrix}\left\{ \begin{matrix}{{{\hat{i}}_{u} = {\underset{i}{argmax}\left\{ p_{i} \right\}}};} & {{i \in I_{\tau,u}};{p_{i} = {\sum\limits_{a = 1}^{A}{y_{i,a}}^{2}}}} \\{{\hat{\tau}}_{u} = {\left( {{\hat{i}}_{u} - C_{u}} \right)T_{S}}} & \;\end{matrix} \right. & (35)\end{matrix}$

where: A is the number of antenna; C_(u) is the cyclic shift of user u;T_(S) is the sampling period of sequence y; and I_(τ,u) is the timingoffset window of user u, defined as:

$\begin{matrix}\left\{ \begin{matrix}{I_{\tau,u} = \left\{ {{- N_{early}},\ldots \;,{- 1},0,1,\ldots \;,N_{late}} \right\}} \\{N_{early} = \left\lceil {{\max \left( {{0.5\mu \; s},\tau_{\max}} \right)}\text{/}T_{S}} \right\rceil} \\{N_{late} = \left\lceil {\left\lbrack {W_{M} + {\max \left( {{0.5\; \mu \; s},\tau_{\max}} \right)}} \right\rbrack \text{/}T_{S}} \right\rceil} \\{W_{M} = {\min \left( {{1\; \mu \; s},\tau} \right)}}\end{matrix} \right. & (36)\end{matrix}$

where: I_(τ,u)(N_(early)+1)=0 coincides with the first sample of thecyclic shift window of user u; ±τ_(max) is the maximum expected timingerror; W_(M) is the main energy region within the user delay spread; andτ is the delay spread of the user. FIG. 42 illustrates this designprinciple of a user's timing offset window. FIG. 42 show a plot of powerdelay profile versus time samples. The main energy region is enlarged onboth sides by the maximum expected timing offset. For the TU channel,the main energy region is the first 1 μS of the user's cyclic shiftwindow. For the PA channel, the main energy region is the delay spreadof the channel which is 0.9 μS.

FIG. 43 is the power delay profiles (PDP) of both TU and PA channels asthey would appear sampled after the IDFT and the cyclic shiftdemultiplex in the absence of noise, for 20, 8 and 4 PRBs SRSbandwidths. FIG. 43 is the average demultiplexed power delay profile forthe TU channel (FIG. 43A) and the PA channel (FIG. 43B) versus delay forvarious SRS bandwidths. FIG. 43A includes three curves: a SRS bandwidthof 20 PRBs resulting in a 0.63 μS mean delay; a SRS bandwidth of 8 PRBsresulting in 0.54 μS mean delay; and a SRS bandwidth of 4 PRBs resultingin 0.95 μS mean delay. FIG. 43B includes three curves: a SRS bandwidthof 20 PRBs resulting in a 0.13 μS mean delay; a SRS bandwidth of 8 PRBsresulting in a 0.093 μS mean delay; and a SRS bandwidth of 4 PRBsresulting in a 0.15 μS mean delay. FIG. 43 illustrates that the narrowerthe SRS bandwidth, the coarser the power delay profile sampling. Thisaffects the resulting mean delay, as measured from these samples.

FIG. 44 plots the timing estimation mean and standard deviation errorsof the described algorithm for both the TU channel and the PA channelwhen varying the SRS bandwidth. The timing uncertainty of the SRS usersis within ±1 μS. FIG. 44A shows the timing offset mean versus signal tonoise ration. FIG. 44B shows the timing offset standard deviation versussignal to noise ratio. Each of FIGS. 44A and 44B show six curves: TUchannel with an SRS bandwidth of 20 PRBs; TU channel with an SRSbandwidth of 8 PRBs; TU channel with an SRS bandwidth of 4 PRBs; PAchannel with an SRS bandwidth of 20 PRBs; PA channel with an SRSbandwidth of 8 PRBs; and PA channel with an SRS bandwidth of 4 PRBs. Sixand 14 SRS users are multiplexed per symbol with the TU channel and thePA channel, assuming the reserved cyclic shift per comb for noiseestimation. FIG. 44 shows for 20 and 8-PRB SRS bandwidths, the timingestimation mean converges as SNR increases to 0 and 0.35 μs for the PAchannel and the TU channel respectively. In the latter case, thiscorresponds to the average delay of the TU channel in the main energyregion, so that the estimator can be considered non-biased in the SNRregion greater than or equal to −5 dB. Similarly, the standard deviationperformance remains steady and below 0.5 μS in the same SNR region andfor the same bandwidth configurations. With a 4-PRB SRS bandwidth, bothmean and standard deviation performances are deteriorated due to theresulting coarse granularity of the PDP sampling. The effect of adjacentusers' spill-over on the timing offset window generates false alarmsresulting in wrong timing estimations irrespective of the SNR value. Asa result, the following conclusions can be drawn:

The proposed low-complexity timing offset estimation algorithm isnon-biased and shows quite steady performance in the SNR region whereSNR is greater than or equal to −5 dB.

For SNRs below −5 dB, it is recommended to cumulate the PDPs ofsubsequent SRSs to achieve the steady state performance of the above SNRregion.

The larger the SRS bandwidth, the better the estimation accuracy(standard deviation).

Tracking timing offsets as large as ±1 μS is impractical with SRSbandwidth as small as 4 PRBs.

FIG. 45 plots the CDF of the timing estimation error from the describedalgorithm for both TU and PA channels at −18, −12, −6 and 0 dB E_(s)/N₀,when varying the SRS bandwidth. From these curves, we extracted the % oftiming offset estimates within 0.5 μS of the main peak. This is reportedin Table 6. The above conclusions are further confirmed and it can bemeasured that in the steady SNR region (SNR greater than or equal to −5dB) and for 20-PRB and 8-PRB SRS bandwidth, ˜85% and close to 100% oftiming offsets estimates are within 0.5 μS of the main peak for the TUchannel and the PA channel.

TABLE 6 SRS −18 dB −12 dB −6 dB 0 dB BW TU PA TU PA TU PA TU PA 20 PRBs 66% 76% 87% 97% 92% 100%  93% 100% 8 PRBs 48% 56% 72% 86% 84% 98% 88%100% 4 PRBs 35% 30% 51% 46% 60% 59% 63%  62%

This patent application describes in details the design choices for theLTE SRS channel, channel gain, noise variance and timing offsetestimators, from theoretical derivations and performance evaluations. Inparticular, the proposed time-domain based channel estimation withgroup-UE cyclic shift de-multiplexing is a low-complexity approach thatretains the inherent noise reduction performance on channel estimateswhile allowing sharing the same upfront computation for users' channels,timing offset estimations and noise variance estimation. The unbiasedchannel gain estimation requires estimating and removing the noisevariance by means of one reserved cyclic shift per SRS comb. Differentnoise removal techniques with negative gain avoidance are assessed.Applying a simple clipping threshold of 0.01 provides the bestperformance compromise across configurations. Further noise reductiontechniques are investigated showing that geometry-based selective cyclicshift window reduction outperforms other approaches such as LMSfiltering. Different techniques to derive per-PRB SNR from the achievedper-antenna per-subcarrier channel gain estimates are evaluated and itis shown that low-complexity arithmetic averaging can be used on PAchannel but should be restricted to very low SNR (less than −5 dB) on TUchannel above which harmonic averaging is mandated. An SRS sub-carrierdecimation factor per comb of up to 3 allows reducing the complexity inthe harmonic averaging computation without noticeable performancedegradation. Comprehensive channel gain and SNR performance resultsobtained from realistic multi-user link-level simulations over a wideSNR range are presented and can be used for further reference in systemsimulations to model the measurement errors from SRS. Reviewing theimpact of timing errors on the above SNR estimator, a simple timingoffset estimator is proposed providing for SNR greater than or equal to−5 dB and SRS bandwidths greater than or equal to 8 PRBs as more than85% of timing offsets estimates within 0.5 μS of the main peak of thechannel. Lower SNRs would need cumulating the Power Delay Profiles ofsubsequent SRSs to achieve the steady state performance of the above SNRregion, and with 4-PRB SRS bandwidth, timing offset estimation should beemployed with smaller than ±1 μS timing uncertainty to avoid erroneousestimates due to adjacent cyclic shift users' spill-over.

FIG. 46 is a block diagram illustrating internal details of an eNB 1002and a mobile UE 1001 in the network system of FIG. 1. Mobile UE 1001 mayrepresent any of a variety of devices such as a server, a desktopcomputer, a laptop computer, a cellular phone, a Personal DigitalAssistant (PDA), a smart phone or other electronic devices. In someembodiments, the electronic mobile UE 1001 communicates with eNB 1002based on a LTE or Evolved Universal Terrestrial Radio Access Network(E-UTRAN) protocol. Alternatively, another communication protocol nowknown or later developed can be used.

Mobile UE 1001 comprises a processor 1010 coupled to a memory 1012 and atransceiver 1020. The memory 1012 stores (software) applications 1014for execution by the processor 1010. The applications could comprise anyknown or future application useful for individuals or organizations.These applications could be categorized as operating systems (OS),device drivers, databases, multimedia tools, presentation tools,Internet browsers, emailers, Voice-Over-Internet Protocol (VOIP) tools,file browsers, firewalls, instant messaging, finance tools, games, wordprocessors or other categories. Regardless of the exact nature of theapplications, at least some of the applications may direct the mobile UE1001 to transmit UL signals to eNB (base-station) 1002 periodically orcontinuously via the transceiver 1020. In at least some embodiments, themobile UE 1001 identifies a Quality of Service (QoS) requirement whenrequesting an uplink resource from eNB 1002. In some cases, the QoSrequirement may be implicitly derived by eNB 1002 from the type oftraffic supported by the mobile UE 1001. As an example, VOIP and gamingapplications often involve low-latency uplink (UL) transmissions whileHigh Throughput (HTP)/Hypertext Transmission Protocol (HTTP) traffic caninvolve high-latency uplink transmissions.

Transceiver 1020 includes uplink logic which may be implemented byexecution of instructions that control the operation of the transceiver.Some of these instructions may be stored in memory 1012 and executedwhen needed by processor 1010. As would be understood by one of skill inthe art, the components of the uplink logic may involve the physical(PHY) layer and/or the Media Access Control (MAC) layer of thetransceiver 1020. Transceiver 1020 includes one or more receivers 1022and one or more transmitters 1024.

Processor 1010 may send or receive data to various input/output devices1026. A subscriber identity module (SIM) card stores and retrievesinformation used for making calls via the cellular system. A Bluetoothbaseband unit may be provided for wireless connection to a microphoneand headset for sending and receiving voice data. Processor 1010 maysend information to a display unit for interaction with a user of mobileUE 1001 during a call process. The display may also display picturesreceived from the network, from a local camera, or from other sourcessuch as a Universal Serial Bus (USB) connector. Processor 1010 may alsosend a video stream to the display that is received from various sourcessuch as the cellular network via RF transceiver 1020 or the camera.

During transmission and reception of voice data or other applicationdata, transmitter 1024 may be or become non-synchronized with itsserving eNB. In this case, it sends a random access signal.

eNB 1002 comprises a Processor 1030 coupled to a memory 1032, symbolprocessing circuitry 1038, and a transceiver 1040 via backplane bus1036. The memory stores applications 1034 for execution by processor1030. The applications could comprise any known or future applicationuseful for managing wireless communications. At least some of theapplications 1034 may direct eNB 1002 to manage transmissions to or frommobile UE 1001.

Transceiver 1040 comprises an uplink Resource Manager, which enables eNB1002 to selectively allocate uplink Physical Uplink Shared CHannel(PUSCH) resources to mobile UE 1001. As would be understood by one ofskill in the art, the components of the uplink resource manager mayinvolve the physical (PHY) layer and/or the Media Access Control (MAC)layer of the transceiver 1040. Transceiver 1040 includes at least onereceiver 1042 for receiving transmissions from various UEs within rangeof eNB 1002 and at least one transmitter 1044 for transmitting data andcontrol information to the various UEs within range of eNB 1002.

The uplink resource manager executes instructions that control theoperation of transceiver 1040. Some of these instructions may be locatedin memory 1032 and executed when needed on processor 1030. The resourcemanager controls the transmission resources allocated to each UE 1001served by eNB 1002 and broadcasts control information via the PDCCH.

Symbol processing circuitry 1038 performs demodulation using knowntechniques. Random access signals are demodulated in symbol processingcircuitry 1038.

During transmission and reception of voice data or other applicationdata, receiver 1042 may receive a sounding reference signal from a UE1001. The sounding reference signal is processed by receiver 1042 toestimate channel state, channel gain, noise power and timing error of UE1001 according to the present invention. In this embodiment, the channelstate, channel gain, noise power and timing error calculation isembodied by executing instructions stored in memory 1032 by processor1030. In other embodiments, the channel state, channel gain, noise powerand timing error calculation may be embodied by a separateprocessor/memory unit, by a hardwired state machine, or by other typesof control logic, for example. In response to receiving the soundingreference signal, eNB 1002 may schedule an appropriate set of resourcesand notifies UE 1001 with a resource grant as well as a timing advancecommand.

What is claimed is:
 1. A wireless communication receiver comprising: aserial to parallel converter receiving a radio frequency signal andgenerating N_(FFT) corresponding serial signals; a fast Fouriertransform device connected to said serial to parallel converterreceiving said N_(FFT) corresponding serial signals and converting saidN_(FFT) corresponding serial signals from a time domain into a frequencydomain; a EZC root sequence unit generating a set of root sequencesignals; an element-by-element multiply unit connected to said fastFourier transform device and said EZC root sequence unit, saidelement-by-element multiply unit forming a set of products including aproduct of each of said frequency domain signals from said fast Fouriertransform device and a corresponding root sequence signal; anN_(SRS)-length IDFT unit connected to said element-by-element multiplyunit performing a group cyclic-shift de-multiplexing of said productsemploying a sounding reference symbol Orthogonal Frequency DivisionMultiplexing Orthogonal Frequency Division Multiple Access symbolstructure and a Constant Amplitude Zero Auto-Correlation sequence tocompute an impulse response for each multiplexed channel through afrequency-domain computed periodic correlation; and a discrete Fouriertransform unit connected to said IDFT unit and receiving cyclic shiftde-multiplexing signals to convert them back to frequency-domain.
 2. Thewireless communication receiver of claim 1, wherein: said group cyclicshift de-multiplexing performed by said discrete Fourier transform unitincludes:Y=F _(N) _(SRS) _(N) _(FFT) ry=F _(N) _(SRS) ⁻¹diag(X*Y ^(T)) where: F_(N) _(SRS) _(N) _(FFT) is aN_(SRS) by N_(FFT) matrix corresponding to N_(FFT)-point FFT and N_(SRS)sub-carriers de-mapping; and F_(N) _(SRS) is a N_(SRS) by N_(SRS)matrix, thereby producing for each SRS comb a concatenated ChannelImpulse Response sequence y of all wireless communication receivesmultiplexed on a same root sequence.
 3. The wireless communicationreceiver of claim 1, wherein: said group cyclic shift de-multiplexingperformed by said discrete Fourier transform unit includes:y _(u)=(0, . . . ,0,y _(n) ₁ _((u)) ,y _(n) ₂ _((u)) , . . . ,y _(n)_(L) _((u)),0, . . . ,0)^(T)Ĥ _(u) =F _(N) _(SRS) y _(u) where: F_(N) _(SRS) is a N_(SRS) by N_(SRS)matrixes corresponding to N_(SRS)-point DFT; and n₁(u), . . . , n_(L)(u)are the samples defining the cyclic shift window of user u, involvingzeroing-out y samples outside the cyclic shift window of user u and laststage N_(SRS)-length DFT-based frequency interpolation.
 4. The wirelesscommunication receiver of claim 1, wherein: said group cyclic shiftde-multiplexing performed by said discrete Fourier transform unitincludes performing Channel Impulse Response extraction and cyclic shiftde-multiplexing simultaneously by selecting the appropriate user'scyclic shift window.
 5. The wireless communication receiver of claim 4,wherein: selecting a cyclic shift window includes shrinking a SRSbandwidth by 10% to minimize the interpolation errors.
 6. The wirelesscommunication receiver of claim 1, further comprising: a non-biasedper-antenna per-sub-carrier channel gain estimator performingĜ ₀(a)=|{circumflex over (H)}(a)|²−{circumflex over (σ)}_(N) ² where:{circumflex over (σ)}_(N) ² is an estimate of the noise variance σ_(N)²=a²σ_(H) ², involving estimating and removing the noise variance. 7.The wireless communication receiver of claim 4, wherein: said noiseremoval includes a negative gain avoidance by applying a simple clippingthreshold of 0.01 according toĜ _(Clip)=max{|{circumflex over (H)}(a)|²−{circumflex over (σ)}_(N) ² ;G_(floor)}.
 8. The wireless communication receiver of claim 1, furthercomprising: a per-antenna time domain noise variance estimator reservinga cyclic shift per SRS comb and averaging the squared noise samplesacross a noise window selected from the samples outside the cyclic shiftwindows of one or more users.
 9. The wireless communication receiver ofclaim 8, wherein: said per-antenna time domain noise variance estimatormaximizes the number of noise samples while not including samplescarrying adjacent users' energy in spill-over regions.
 10. The wirelesscommunication receiver of claim 8, wherein: said per-antenna time domainnoise variance estimator maximizes a UE-geometry-based selective cyclicshift window reduction as: NOISE REDUCTION TECHNIQUE LMS CYCLIC SHIFTWINDOW FILTERING SHRINK Channel Model TU PA TU PA Channel estimation MSE3 dB  3 dB 6 dB  6 dB Channel gain mean error 2 dB 1.2 dB 2.1 dB  2.5dB  Channel gain standard 1 dB 0.5 dB 1 dB 1.2 dB. deviation


11. The wireless communication receiver of claim 1, further comprising:a per-chunk signal to noise ratio (SNR) estimator from the achievedper-antenna per-subcarrier channel gain estimates based on selectivelyusing a selected one of low-complexity arithmetic averaging or harmonicaveraging depending on both the channel type and the UE's SNR.
 12. Thewireless communication receiver of claim 1, further comprising: a timingoffset estimator combining the amplitude delay profiles across antennasfrom the concatenated delay profiles sequence y and searching for thehighest peak in the user's timing offset window according to:$\quad\left\{ \begin{matrix}{{{\hat{i}}_{u} = {\underset{i}{argmax}\left\{ p_{i} \right\}}};} & {{i \in I_{\tau,u}};{p_{i} = {\sum\limits_{a = 1}^{A}{y_{i,a}}^{2}}}} \\{{\hat{\tau}}_{u} = {\left( {{\hat{i}}_{u} - C_{u}} \right)T_{S}}} & \;\end{matrix} \right.$ where: A is the number of antenna; C_(u) is thecyclic shift of user u; T_(S) is the sampling period of sequence y; andI_(τ,u) is the timing offset window of user u, defined as:$\quad\left\{ \begin{matrix}{I_{\tau,u} = \left\{ {{- N_{early}},\ldots \;,{- 1},0,1,\ldots \;,N_{late}} \right\}} \\{N_{early} = \left\lceil {{\max \left( {{0.5\mu \; s},\tau_{\max}} \right)}\text{/}T_{S}} \right\rceil} \\{N_{late} = \left\lceil {\left\lbrack {W_{M} + {\max \left( {{0.5\; \mu \; s},\tau_{\max}} \right)}} \right\rbrack \text{/}T_{S}} \right\rceil} \\{W_{M} = {\min \left( {{1\; \mu \; s},\tau} \right)}}\end{matrix} \right.$ where: I_(τ,u)(N_(early)+1)=0 coincides with thefirst sample of the cyclic shift window of user u; ±τ_(max) is themaximum expected timing error; W_(M) is the main energy region withinthe user delay spread; and τ is the delay spread of the user.